Appendix: A Probabilistic State Space Model for Joint Inference from Differential Equations and Data Nicholas Krämer University of Tübingen University of Tübingen Tübingen, Germany

This section provides detailed information about the state-space model and approximate Gaussian inference therein. Appendix A.1 defines the augmented state-space model that formalizes the dynamics of the Gauss-Markov processes introduced in Section 3.1. Appendix A.2 provides the equations for prediction and update steps of the extended Kalman filter in such a setup, which is described in Section 3.4 (in particular, Algorithm 1). A.1 Augmented state-space model Section 3 describes the joint inference of both a latent process u(t): [t The measurement models are given in Eq. (6) (for observed data) and in Eq. (7) (for ODE measurements). In the experiments presented in Sections 5.2 and 5.3 we model the latent contact rate β(t) as a Matérn-3 More details on the use of integrated Wiener processes in probabilistic ODE solvers can be found in, for instance, the work by Kersting et al. [5].